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Unformatted text preview: 0 0 1.05 0.90 Corresponding price vector (ps) = ( 1 1 0 0 0 0 ) ii) p_atom = ps * inv (Q) p_atom = ( 0.3571 0.5952 0.1276 0.2126 0.2126 0.3543) iii) Assuming that I have purchased the European call option, iv) We can price the option by constructing a portfolio of elemental payment combinations that generates the same vector c. It follows from the no-arbitrage condition (as well as LOP) that the replicating portfolio and option should have the same price. In fact, once we have calculated the atomic price vector, it is not even necessary to construct a replicating portfolio. The arbitrage-free price of the option can be calculated directly by simply multiplying the atomic price vector by the time-state vector, c, implied by the option (assuming it is exercised optimally). Call = ( 0 0 0.64 0.12 0.12 0) P call= p_atom * call p_call = 0.1327 v) Assuming that I have purchased the European put option vi) Call= (0 0 0 0 0 0.24) P call= p_atom * call p_call = 0.0850...
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